Of all the men, and one woman, who have been prime minister since Sir Robert Walpole, we can debate who was the best or the worst, cleverest or stupidest, noblest or basest. After he had written a biography of Gladstone, arguably the greatest, Roy Jenkins thought he could only continue with Churchill, the most extraordinary human being ever to hold the office.

But if there were a supper table game to decide who was the oddest person ever to reach Number 10, it would be no contest: the answer could only be Jenkins's Balliol contemporary, Edward Heath. The puzzle about him is not why he lost three out of the four elections he fought as Conservative leader, or why he was deposed in 1975 by Margaret Thatcher, but how on earth he became prime minister. Philip Ziegler's new life of Heath is characteristically accomplished and thorough, but it has few answers to the mystery of Heath's personality.

No clues are found in the early years. The cosseted carpenter's son from Broadstairs became a scholarship boy at grammar school and Oxford, where he played the organ, turned himself into a passable if unexciting public speaker and became president of the Union. Joining the army in 1940, Heath served creditably as a Royal Artillery officer from Normandy to the Rhine. One startling episode, unmentioned until he published his otherwise numbingly dull memoirs, was when Heath commanded a firing squad which shot a young Polish soldier court-martialled for rape.

After demob and several odd jobs (the most unlikely at the Church Times), Heath was elected MP for Bexley in 1950, appointed a junior whip before the Tories returned to office the following year, and by December 1955 was chief whip. Of all government jobs, this requires firmness and fairness allied to tact and patience and Heath's ascent seems baffling in hindsight. He later became a byword for graceless petulance and sheer rudeness, at dinner "apt to relapse into morose silence or completely ignore the woman next to him and talk across her to the nearest man".

In 1965, for the first time, the Tory party leader was elected by MPs. But they didn't know quite how to handle the election and Heath won almost by default. His relationship with his party was fraught from the start; as Ziegler says, "his loathing for his Conservative opponents was more intense" than any hostility to Labour.

It was another surprise when Heath won the 1970 election. For a year or two, it was plain sailing, until his government hit a political perfect storm (an apter phrase than usual for a man whose private passion was sailing). Unemployment and inflation rose sharply, militant unions challenged the government, violence escalated in Ulster. To have mastered all this would have required political skill of a high order, which Heath rarely displayed. He was preoccupied with joining the Common Market (which even Europhiles must admit involved misrepresentation on his part), and his failings of temperament aggravated every other problem. He tacked this way and that, until wrecked by the fiasco of the three-day week and the mistimed 1974 election. Then came his defeat by Mrs Thatcher and the tragi-ludicrous sulk which lasted the rest of his life.

And a lonely life at that. It was an ironical comment on the permissive society, Bernard Levin wrote at the time in the Observer, that we had had to wait until the 1970s for a prime minister who was a virgin. Levin had forgotten Pitt the Younger and Balfour, both bachelors with no known amorous interests, but he was doubtless right about Heath. There was inevitable muttering that he might be homosexual, but Ziegler concludes that he was simply asexual.

Readable and judicious as it is, the book is not without lapses. "Humphrey Berkeley" is sometimes so spelled and sometimes correctly as "Humphry". And Ziegler has Roy Jenkins resigning from the Labour cabinet in 1975. He in fact resigned from the shadow cabinet in 1972, but returned to government in 1974 until he left in 1976.

Only the most loyal biographer could call Heath a successful politician, an appealing fellow or even an interesting person. Maybe in the end, there is no mystery to this odd man. If Napoleon III, in Bismarck's phrase, was the Sphinx without a riddle, Ted Heath was the enigma without any variations.

Geoffrey Wheatcroft's most recent book is Yo, Blair! (Politico).

The blurb for Philip Ziegler's workmanlike new biography tells us that Heath was "the most enigmatic of our former prime ministers". At first I thought this was publisher's hype, but the more I brooded on it, the more accurate it seemed. Heath was indeed an enigma  to himself, I suspect, as well as to others. He was a man of driving ambition and relentless will who seemed incapable of learning the elementary skills of his craft. He could be kindly and considerate, but also abominably rude and insufferably arrogant. As befitted the son of a small businessman, he was a lifelong Conservative. Yet as an Oxford student in the 1930s, he was a disciple of the Labour-voting master of Balliol, "Sandy" Lindsay, and of the Labour churchman William Temple, later Archbishop of Canterbury.

The Balliol organ scholar was father to Heath the prime minister. He patently despised the Conservative party and preferred the company of trades-union leaders to that of the business elite: it was not an accident that his one memorable phrase was "the unacceptable face of capitalism". Philosophically, he belonged to the relaxed and evolutionary whig tradition exemplified by grandees such as Harold Macmillan and Anthony Eden, but in temperament he was an odd mixture of managerial technocrat and Fabian interventionist. As a young Labour backbencher throughout the four years of his prime ministership, I viewed him with a kind of baffled admiration. Ziegler's biography has left me as baffled  and as admiring  as before.

Ziegler makes it abundantly clear that Heath was responsible for the most decisive turning point in postwar British history: belated entry into what was then the European Community and is now the European Union. No one else could have secured it. Macmillan tried and failed. Wilson would have liked to try, but he would never have won over the suspicious Georges Pompidou. Heath did win him over  not through charm or diplomatic finesse, but because he made it clear that he shared the French vision of Europe's place in the world and the visceral French conviction that European ties should trump Atlantic ones. It was a momentous achievement that changed the British constitution, the British state and the British way of life for ever.

But it was also a mysterious one. Politically speaking, Europe was the great passion of Heath's life, but the emotional roots of his Europeanism are far from obvious. How did the gawky, linguistically maladroit, lower middle-class Broadstairs boy discover the European vocation that gave him his place in British history? This is the great puzzle of Heath's political life, and Ziegler does not solve it. He recounts the facts with style and skill. We see the undergraduate Heath travelling on the continent, watching a Nuremberg rally in horror, shaking Himmler's "drooping and sloppy" hand, and managing to get back to England from Poland only a week before war broke out. Later, we watch the 29-year-old artillery officer fighting his way from Normandy to Belgium, taking charge of a prisoner of war camp in defeated and devastated Germany, and travelling across the country to watch the Nuremberg trials.

All this must have left an indelible impression on a young, still unformed man; and Ziegler makes that clear. But he doesn't probe beneath the surface Heath to explore the inner meaning of his wartime and pre-war experiences, or to tease out the emotional links between them and his lifelong vision of a united Europe. Later he writes that the true Heath lay somewhere "between the sublime and the mundane". It was the sublime Heath  the Heath of imagination, conviction and passion  who took Britain into the European Community, but all too often Ziegler allows the mundane Heath to dominate the proceedings.

The same applies to the other great mystery of Heath's prime ministership  the famous U-turn from watered-down neo-liberalism to industrial intervention, wage controls and a doomed attempt to introduce a form of tripartite economic governance. From the vantage point of 2010, the U-turn seems a trumpery affair: the feeble last hurrah of the doomed postwar consensus that the Thatcher revolution was destined to sweep away. But at the time it seemed a Damascene conversion, comparable with Robert Peel's repeal of the corn laws in 1846. Having gained power on the ticket of free collective bargaining and state disengagement from industry, the government suddenly stood on its head  becoming more interventionist than its Labour predecessor and imposing a statutory wage freeze into the bargain.

This, too, was Heath's doing  and at the same time his undoing. For all practical purposes he became the last social-democratic prime minister of Britain. But in the process he dug his own political grave, and paved the way for the long neo-liberal hegemony that started with Thatcher and still endures. The great U-turn was not sublime, exactly, but neither was it mundane. A vision of social peace and cross-class collaboration lurked between the lines of Heath's strangulated rhetoric in the dying days of his prime ministership; and that vision, like his Europeanism, patently sprang from the better angels of his nature. If Ziegler had only uncovered its sources he would have written a great book. As it is, he has written a highly enjoyable and sometimes gripping one.

David Marquand's Britain Since 1918: The Strange Career Of British Democracy is published by Phoenix.